Question

Use the information given in the adjoining figure to find:

(i)The length of AC.

(ii)The are a of $\Delta ABC.$

(iii)The length of BD, correct to one decimal place.

Answer 1

AB=24 cm, BC=7 cm

$\left(i\right)AC=\sqrt{A{B}^2+B{C}^2}$

$=\sqrt{{24}^2+7^2}$

$=\sqrt{576+49}$

$=\sqrt{625}=24cm$

(ii)Area of $\Delta ABC=\frac{1}{2}AB\times BC$

$=\frac{1}{2}\times 24\times 7=84c{m}^2$

$\left(iii\right)BD\perp AC$

Area $\Delta ABC=\frac{1}{2}AC\times BD$

$84=\frac{1}{2}\times 25\times BD$

$\Rightarrow BD=\frac{84\times 2}{25}=\frac{168}{25}=6.72cm$

=6.7 cm